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Dampened Oscillations

  1. Nov 2, 2007 #1
    1. The problem statement, all variables and given/known data
    A hard-boiled egg moves on the end of a spring with force constant k. It is released with an amplitude 0.300 m. A damping force [tex]F_x = -bv[/tex] acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.
    [itex]m = 50.0g[/itex] (0.05kg)
    [itex]k = 25.0N/m[/itex]

    Calculate the magnitude of the dampening coefficient b.

    2. Relevant equations
    [tex]F = ma[/tex]

    [tex]F = -kx[/tex]

    [tex]v = \frac{dx}{dt}[/tex]

    [tex]a = \frac{dv}{dt}[/tex]

    [tex]F_x = -bv[/tex]

    There is another that I can't remember for sure... IF I'm right, it goes like this:
    [tex]y_0 = A_0 e^{-t/\tau}[/tex]

    3. The attempt at a solution
    First, I don't know how the egg "moves". Is it hanging vertically, in which I can take [itex]a = g = 9.81m/s[/itex]? Or what other orientation is it in?

    Secondly, while I'm fairly sure I need to use [itex]y_0 = A_0 e^{-t/\tau}[/itex], like I did in my Physics Lab, I'm not too sure how the variable b comes into all of this. I was taught that [itex]\tau[/itex] helped control the dampening of an oscillation, and was measured in seconds, or something similar.

    This is as far as I've gotten. Not sure where to turn next.
     
  2. jcsd
  3. Nov 2, 2007 #2

    Astronuc

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    Staff: Mentor

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